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Round seventeen over thirty-six to the nearest quarter.
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Now we’ve been given a number between zero and one, and we’ve got to round it to the nearest quarter.
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Well first, let’s imagine a scale from zero to one.
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Now if we mark that off in quarters, we’ve got zero, one quarter, two quarters, three quarters, or four quarters.
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Well zero is just zero, one quarter is just one quarter.
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But two quarters, we can simplify to a half.
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Three quarters doesn’t simplify, and four quarters is the same as one.
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So what we’ve got to do in this question is decide, which one of those seventeen thirty-sixths is nearest.
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Now I’m just gonna think about how many thirty-sixths represent each of those fractions.
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Well no thirty-sixths is representing zero.
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And thirty-six thirty-sixths would represent one.
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And a half of thirty-six is eighteen, so eighteen thirty-sixths represents a half.
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And a quarter is half of a half, so half of eighteen is nine, so nine thirty-sixths represents one quarter.
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And that leaves us with three quarters.
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Well three times one quarter would be three quarters, so three lots of nine thirty-sixths are twenty-seven thirty-sixths.
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So whereabouts on that scale would seventeen thirty-sixths sit?
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Well it would sit in here somewhere.
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It’s bigger than nine thirty-sixths, but it’s less than eighteen thirty-sixths.
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So which is it nearer to, eighteen thirty-sixths, or nine thirty-sixths?
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Well the difference between seventeen thirty-sixths and eighteen thirty-sixths is just one thirty-sixth.
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But the difference between nine thirty-sixths and seventeen thirty-sixths is eight thirty-sixths.
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So seventeen thirty-sixths is much closer to eighteen thirty-sixths than nine thirty-sixths.
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And remember, eighteen thirty-sixths is the same as two quarters, which is equivalent to a half.
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So to the nearest quarter, we could say it’s two quarters, but we’d probably simplify that to a half.
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So our answer is, rounded to the nearest quarter, seventeen thirty-sixths, is approximately equal to a half.